ICloud Drive and Photos Library

What is the function of iCloud Drive , you can see this in the article https://support.apple.com/en-in/guide/icloud/mmd0b4a7f5e8/icloud

And not to store complete photo library with massive photos that's the reason ineligible icon is appearing https://support.apple.com/en-in/guide/mac-help/mchlp1774/10.14/mac/10.14

To back up the photo library see the article https://support.apple.com/en-in/guide/photos/pht6d60d10f/mac

Besides iCloud photos to sync my photos between devices I use Time Machine to backup my Mac. TimeMachine backups include your photo library.

A backup of your iCloud Photos Library on iCloud Drive will be no good, even if the Photos Library were small enough to be uploaded to iCloud Drive. A Photos Library will be damaged by the cloud syncing. It is not safe to store it there - the same goes for Dropbox or Google drive.

See: Updating from iPhoto to Photos for macOS – Apple Support

 If you store your Photos library in a location that's part of a cloud service (for example, Dropbox, Box, or Google Drive), your library might be damaged by the syncing process. As a result, you could lose photos.

To see your photos on all your devices, you can use iCloud Photo Library. To back up your library, you can use Time Machine.

And also:

Move your Photos library to save space on your Mac - Apple Support